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In Manifolds and Complex Surfaces PDFSmale established the generalized Poincare Conjecture Manifolds and PDF #8608 in dimensions greater than or eual toand proceeded to prove the h cobordism theorem This result inaugurated a major effort to classify all possible smooth and topological structures on manifolds of dimension at least By the mid 's the main outlines of this theory were complete and explicit answers especially concerning simply connected manifolds as Smooth Four PDF well as general ualitative results had been o.

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Smooth Four Manifolds and Complex Surfaces Ergebnisse der Mathematik und ihrer Grenzgebiete 3 FolgeA Series of Modern Surveys in MathematicsBtained As an example of such a ualitative result a closed Four Manifolds and Complex Surfaces Epubsimply connected manifold of dimensionis determined up to finitely many diffeomorphism possibilities by its homotopy type and its Pontrjagin classes There are similar results for self diffeomorphisms which at least in the simply connected case say that the group of self diffeomorphisms of a closed manifold M of Four Manifolds and ePUB #180 dimension at least is commensurate with an arithmetic subgroup of the linear algebraic.